$$\mathop {Lim}\limits_{x \to \infty } {{{x^3} - \cos x} \over {{x^2} + {{\left( {\sin x} \right)}^2}}} = \_\_\_\_\_\_.$$

Let $$R$$ be a symmetric and transitive relation on a set $$A$$. Then

A bag contains 10 white balls and 15 black balls. Two balls drawn in succession. The probability that one of them is black the other is white is

The number of elements in the power set $$P(S)$$ of the set $$S = \left\{ {\left\{ \phi \right\},1,\left\{ {2,3} \right\}} \right\}$$ is